Yes, your credit will affect your ability to get financing in order to purchase a home. Your best bet is the get an honest and credible assessment from a good mortgage rep. who can help you understand what you can afford, and if your credit is an obstacle make recommendations to get you on track.
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There are outstanding rentals in both towns. As with any life choice, what makes for a great selection is the attention to the details. It's critical to work with an agent that will understand your needs extensively so they can advise you well. You don't want an agent that will make decisions for you, but you will want one that lays out the implications of both towns (the vibe, the lifestyle, etc), individual neighborhoods, commute times, school choices, etc so you can make the very best decision for your family.
It's very easy to make pat answers in a formulaic manner and you shouldn't settle for that. I suggest you work with local experts (I've lived in Millburn for 15 years) so you can learn for yourself what a good value is or is not.
Unpopular Realtor Comment Coming: Selecting an agent should be treated as hiring someone for a specific job. Interview prospective agents, learn their qualifications, style, professionalism, education, experience, etc.
Many people settle on the first agent they come across because they feel all agents are alike. When one interviews agents, one quickly learns that not all agents are the same!
I cover South Monmouth County--Ocean Grove to Mantoloking. When my daughter was getting married 2 years ago, we tried to find a home, to no avail. Most of the homes won't rent out for weddings and do not rent out for only a weekend. I do have a nice rental off the beach in Spring Lake that does rent short term, but the yard isn't that big, either. And, most of the towns won't let you get married on the beach, but will allow it on the boards. The homes close to the beach rent for $10K/week, fyi. There just aren't too many of them.
We found a couple of houses in Bay Head that looked like possibilities at that time, but they were not oceanfront so we never checked them out totally.
You might want to check into some of the for rent by owner sites to see if there's anything there. Good luck with your search, and blessings on your upcoming marriage.
By the way, my daughter got married at a fabulous estate out Western Monmouth County. If you'd like the details, email me through my site or Trulia profile.... more